Although the Doctor has stated that Time Lords "can live forever, barring accidents," ("The War Games"), they are not immortal. They may be killed in any of the standard ways (ref. the Time War), and death may occur if the mortal injury occurs too quickly for regeneration to happen ("Turn Left") or if the Time Lord is killed during regeneration (implied in "The Impossible Astronaut"). Certain things may also prevent regeneration from taking place, such as anesthetic ("Doctor Who").
Certain chemcials which may not harm humans are fatal to Gallifreyans. ("The Mind of Evil").
Beyond these circumstances, there is also the artifically imposed limit on regenerations. The 13-life limit exists so that Time Lords don't become immortal. First revealed in "The Deadly Assassin", the limit was confirmed to be artificial and not natural in "The Five Doctors" when it was established that the High Council has the ability to grant new regeneration cycles. Initially, the Master is offered one (after his use of other methods to extend his life beyond his 13th incarnation as seen in "The Keeper of Traken"); though this did not occur at that point, "The Sound of Drums" later confirmed that he had been given a new regeneration cycle by the Time Lords. The Doctor was similarly granted a new regeneration cycle in "The Time of the Doctor". Alternately, it is also possible for Time Lords to expel their regeneration energy, allowing them to be unable to regenerate, as River Song did in "Let's Kill Hitler", leading to her death in "Forest of the Dead". The Master was seen to will himself not to regenerate in "Last of the Time Lords" but later events ("The End of Time") suggested this was a ploy rather than a genuine suicide.
The death of a Time Lord at the final end of a regeneration cycle was depicted on screen for the first time in "The Twin Dilemma".